How did you install SketchUp? Sounds like you might be trying to run SketchUp directly from the disk image. The proper way to install is to double click the installer disk image, then in the window that opens drag the SketchUp icon into the Applications Folder icon next to it and drop it there.
For the Auth token problem , there seems to have been an outage or hiccup on the licensing server at some point recently, it should be solved by simply logging out via Help menu>sign out and then signing back in.
Does the SketchUp Pro 2020 application actually get removed from your Applications folder? Shutting down the system by any means (including when the power is lost such as a battery losing sufficient charge) won’t do that. Perhaps @endlessfix is correct that you are running the application from a mounted disk image (rather than the actual Applications folder) and the reboot of the system dismounts the disk image.